--- res: bibo_abstract: - We consider random matrices of the form H=W+λV, λ∈ℝ+, where W is a real symmetric or complex Hermitian Wigner matrix of size N and V is a real bounded diagonal random matrix of size N with i.i.d.\ entries that are independent of W. We assume subexponential decay for the matrix entries of W and we choose λ∼1, so that the eigenvalues of W and λV are typically of the same order. Further, we assume that the density of the entries of V is supported on a single interval and is convex near the edges of its support. In this paper we prove that there is λ+∈ℝ+ such that the largest eigenvalues of H are in the limit of large N determined by the order statistics of V for λ>λ+. In particular, the largest eigenvalue of H has a Weibull distribution in the limit N→∞ if λ>λ+. Moreover, for N sufficiently large, we show that the eigenvectors associated to the largest eigenvalues are partially localized for λ>λ+, while they are completely delocalized for λ<λ+. Similar results hold for the lowest eigenvalues. @eng bibo_authorlist: - foaf_Person: foaf_givenName: Jioon foaf_name: Lee, Jioon foaf_surname: Lee - foaf_Person: foaf_givenName: Kevin foaf_name: Schnelli, Kevin foaf_surname: Schnelli foaf_workInfoHomepage: http://www.librecat.org/personId=434AD0AE-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0003-0954-3231 bibo_doi: 10.1007/s00440-014-0610-8 bibo_issue: 1-2 bibo_volume: 164 dct_date: 2016^xs_gYear dct_language: eng dct_publisher: Springer@ dct_title: Extremal eigenvalues and eigenvectors of deformed Wigner matrices@ ...